BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F09%3A00035397" target="_blank" >RIV/00216224:14310/09:00035397 - isvavai.cz</a>

Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS

Popis výsledku v původním jazyce

In this paper a 3-dimensional system of autonomous differential equations is studied. It can be interpreted as an idealized macroeconomic model with foreign capital investment or an idealized model of the firm profit. The system has three endogenous variables with only one non-linear term and can be also interpreted as an extended van der Pol's equation. It's shown that this simple system covers several types of bifurcations: both supercritical and subcritical Hopf bifurcation and generalized Hopf bifurcation as well, the limit cycle exhibits period-doubling bifurcation as a route to chaos. Some results are analytical and those connected with chaotic motion are computed numerically with continuation programs Content, Xppaut and Maple. We present conditions for stability of the cycles, hysteresis, explore period doubling and using Poincare mapping show a three period cycle that implies chaos.

Název v anglickém jazyce

BIFURCATION ROUTES TO CHAOS IN AN EXTENDED VAN DER POLS EQUATION APPLIED TO ECONOMIC MODELS

Popis výsledku anglicky

In this paper a 3-dimensional system of autonomous differential equations is studied. It can be interpreted as an idealized macroeconomic model with foreign capital investment or an idealized model of the firm profit. The system has three endogenous variables with only one non-linear term and can be also interpreted as an extended van der Pol's equation. It's shown that this simple system covers several types of bifurcations: both supercritical and subcritical Hopf bifurcation and generalized Hopf bifurcation as well, the limit cycle exhibits period-doubling bifurcation as a route to chaos. Some results are analytical and those connected with chaotic motion are computed numerically with continuation programs Content, Xppaut and Maple. We present conditions for stability of the cycles, hysteresis, explore period doubling and using Poincare mapping show a three period cycle that implies chaos.

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2009

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Electronic Journal of Differential Equations

ISSN

1072-6691

e-ISSN

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Svazek periodika

2009

Číslo periodika v rámci svazku

53

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

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Kód UT WoS článku

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EID výsledku v databázi Scopus

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